A review of the literatures on the theory of chromatography is carried out by dividing the subject into four categories : （1） single solute system, (2) multicomponent system, (3) adiabatic adsorption process, and (4) effect of diffusion and/or non-equilibrium. Each part presents a historical survey as well as a critical review of recent advances in the field. Developments in the mathematical theory of quasilinear partial differential equations are also discussed in connection with their applications to the theory of chromatography and other related fields.